40
Views
1
CrossRef citations to date
0
Altmetric
Articles

A note on fractional calculus and the image method for dielectric spheres

Pages 1179-1188 | Published online: 03 Apr 2012

References

  • Maxwell J. C. , Treatise on Electricity and Magnetism , Vol. 1 , reprint by Dover Publication , New York , part 1, ch. 11 , 1954 .
  • Smythe , W. R. 1969 . Static and Dynamic Electricity , 3rd Edition , New York : McGraw-Hill .
  • Lindell , I. V. 1992 . Electrostatic image theory for the dielectric sphere . Radio Science , 27 ( No. 1 ) January-February : 1 – 8 .
  • Lindell , I. V. , C-E. Sten , J. and Kleinman , R. E. December 1992 . “ Low-frequency image theory for the dielectric sphere ” . In Electromagnetic Laboratory Report No. 131 , December , Helsinki University of Technology . The reference by C. Neumann is cited in this report by Lindell et al. The reference by Neumann is: C. Neumann, Hydrodynamische Untersuchungen nebst einem anhange über die Probleme der Elektrostatik und der Magnetischen Induction, Teubner, Leipzig, 1883
  • Oldham , K. B. and Spanier , J. 1974 . The Fractional Calculus , New York : Academic Press .
  • McBride , A. C. and Roach , G. F. , eds. 1985 . Fractional Calculus, Research Notes in Mathematics , Boston : Pitman Advanced Publishing Program .
  • Davis , H. T. 1936 . The Theory of Linear Operators , 64 – 75 . Bloomington , Indiana : The Principia Press . and 276–292
  • Abel , N. H. 1881 . “ Solution de quelques problèmes à l'aide d'intégrales définites ” . In Oeuvres Complètes , Vol. 1 , 16 – 18 . Christiana , , Norway : Grondahl . This reference is cited in [5]
  • Lützen , J. 1984 . “ Liouville's differential calculus of arbitrary order and its electrodynamical origin ” . In Proceedings of the Nineteenth Nordic Congress of Mathematicians Reykjavik published by the Icelandic Mathematical Society, 149–160, 1985
  • Engheta , N. 1994 . Fractional Differintegrals and Electrostatic Fields and Potentials near Sharp Conducting Edges . the ecole d'été Internationale sur Geometrie Fractale et Hyperbolique, Derivation Fractionnaire et Fractale, Applications dans les Science de l'Ingenieur et en Economie . July 3–8 1994 , Bordeaux , France. Also as a part of a talk given by this author at the 1992 IEEE AP-S/URSI International Symposium, Chicago, Illinois, July 17–20, 1992. The talk was entitled "On the role of non-integral (fractional) calculus in electrodynamics," by N. Engheta. The one-page abstract of the talk appeared in the Digest of Symposium, Vol. URSI Digest, p. 163
  • Love , E. R. 1971 . Fractional derivatives of imaginary order . J. London Math. Soc. , 3 Feb. : 241 – 259 . Part 2, Second Series
  • Riemann , B. 1953 . “ Versuch einer allgemeinen Auffasung der Integration und Differentiation ” . In The Collected Works of Bernhard Riemann , 2nd ed. , Edited by: Heinrich , Weber . 353 – 365 . New York : Dover . Chapter 19
  • Liouville , J. 1832 . Mémoire: Sur le Calcul des Différentielles à Indices Quelconques . J. Ecole Polytechn. , 13 : 71 – 162 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.